What is the general solution for 3sin(x+20)-0.75=0 ?

The general solution for 3sin(x+20)-0.75=0 is x=0.25268…+360n-20,x=180-0.25268…+360n-20

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Popular >

3sin(x+20)-0.75=0

Solution

3 sin (x + 2 0^{\circ}) - 0.75 = 0

Solution

x = 0.25268 \dots + 36 0^{\circ} n - 2 0^{\circ}, x = 18 0^{\circ} - 0.25268 \dots + 36 0^{\circ} n - 2 0^{\circ}

Radians

x = 0.25268 \dots - \frac{π}{9} + 2 πn, x = π - 0.25268 \dots - \frac{π}{9} + 2 πn

Solution steps

3 sin (x + 2 0^{\circ}) - 0.75 = 0

Move

0.75

to the right side

3 sin (x + 2 0^{\circ}) - 0.75 = 0

Add

0.75

to both sides

3 sin (x + 2 0^{\circ}) - 0.75 + 0.75 = 0 + 0.75

Simplify

3 sin (x + 2 0^{\circ}) = 0.75

3 sin (x + 2 0^{\circ}) = 0.75

Divide both sides by

3

3 sin (x + 2 0^{\circ}) = 0.75

Divide both sides by

3

\frac{3 sin ( x + 2 0 ^{\circ} )}{3} = \frac{0.75}{3}

Simplify

sin (x + 2 0^{\circ}) = 0.25

sin (x + 2 0^{\circ}) = 0.25

Apply trig inverse properties

sin (x + 2 0^{\circ}) = 0.25

General solutions for

sin (x + 2 0^{\circ}) = 0.25

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x + 2 0^{\circ} = arcsin (0.25) + 36 0^{\circ} n, x + 2 0^{\circ} = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n

x + 2 0^{\circ} = arcsin (0.25) + 36 0^{\circ} n, x + 2 0^{\circ} = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n

Solve

x + 2 0^{\circ} = arcsin (0.25) + 36 0^{\circ} n : x = arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

x + 2 0^{\circ} = arcsin (0.25) + 36 0^{\circ} n

Move

2 0^{\circ}

to the right side

x + 2 0^{\circ} = arcsin (0.25) + 36 0^{\circ} n

Subtract

2 0^{\circ}

from both sides

x + 2 0^{\circ} - 2 0^{\circ} = arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

Simplify

x = arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

x = arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

Solve

x + 2 0^{\circ} = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n : x = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

x + 2 0^{\circ} = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n

Move

2 0^{\circ}

to the right side

x + 2 0^{\circ} = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n

Subtract

2 0^{\circ}

from both sides

x + 2 0^{\circ} - 2 0^{\circ} = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

Simplify

x = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

x = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

x = arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}, x = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

Show solutions in decimal form

x = 0.25268 \dots + 36 0^{\circ} n - 2 0^{\circ}, x = 18 0^{\circ} - 0.25268 \dots + 36 0^{\circ} n - 2 0^{\circ}

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Frequently Asked Questions (FAQ)

What is the general solution for 3sin(x+20)-0.75=0 ?
The general solution for 3sin(x+20)-0.75=0 is x=0.25268…+360n-20,x=180-0.25268…+360n-20